Question

A drum rotates around its central axis at an angular velocity of 12.60 rad/s. If the drum then slows at a constant rate of 4.20 rad/s 2 , (a) how much time does it take and (b) through what angle does it rotate in coming to rest

Answer 1

(a) t=3s

(b) β=18.9rad

Step-by-step explanation:

Given data

`wo_(angular-velocity)=12.60 rad/s\\ \alpha_(angular-acceleration)=-4.20rad/s^(2)`

Part(a)

From the equation of angular motion to find time

So:

`w=w_(o)+\alpha t\\0=12.60rad/s+(-4.20rad/s^(2) ) t\\-4.20 t=-12.60\\t=3s`

Part(b)

From the equation of simple motion to find angle β

So

`\beta=w_(o)t+(1/2)\alpha t^(2)\\\beta=(12.60rad/s)(3)+(1/2)(-4.20rad/s^(2) ) (3s)^(2)\\ \beta =18.9rad`